On passage to the limit in a~multistage multiphase synthesis of substance

D. N. Shtokalo

Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 4, pp. 135-146.

Résumé

We presenta scheme of the proof of passage to the limit to a delayed equation in a model of multistage synthesis of substance when the number of stages increases with the preservation of the time of the whole synthesis when the chain of the synthesis reactions splits into phases. Each phase is characterized by constants defining the intensity of the direct and reverse processes and sinks. It is shown that if the intensity of the direct process dominates the reverse process on each phase with unrestricted number of stages then, when the total number of stages increases, the function that determines the synthesized substance and is defined by the last component of the vector of the solution to the system of ordinary differential equations converges uniformly to the function of the solution to the delayed equation. Numerical estimates of the uniform convergence are obtained for specific values of the parameters.

Détail

Keywords: multistage synthesis of substance, passage to the limit, delayed equation.

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